One-dimensional Josephson junction arrays: Lifting the Coulomb blockade by depinning

Experiments with one-dimensional arrays of Josephson junctions in the regime of dominating charging energy show that the Coulomb blockade is lifted at the threshold voltage, which is proportional to the array's length and depends strongly on the Josephson energy. We explain this behavior as depinning of the Cooper-pair-charge-density by the applied voltage. We assume strong charge disorder and argue that physics around the depinning point is governed by a disordered sine-Gordon-like model. This allows us to employ the well-known theory of charge density wave depinning. Our model is in good agreement with the experimental data.

Figure 1

Hysteretic $I-V$ characteristics of array B255 measured for increasing voltages (blue) and decreasing voltages (red) at $\mathrm{\Phi }=0$. The left inset shows an SEM micrograph of the Josephson junction array; the right inset is a schematic representation of the array. The middle inset displays the probability density function of $V_{\text{sw}}$.

Figure 2

The switching voltage normalized to the array length $N$ as a function of the magnetic flux $\mathrm{\Phi }$ for three arrays of length 255. Solid lines are fitted functions; circles show experimental data.

Figure 3

Sketch of the Josephson junction array with inductances $L_0$. The magnified part shows the distribution of the charges $q_i^g, q_i, 2n_i$, and $f_i$ on the island and the capacitances. In the language of electrical circuits the background charge $f_i$ is given by the constant charge on an additional capacitance that is connected to the island, as shown in red in the magnified sketch of the island above.

Figure 4

The dimensionless strength of the pinning potential $\tilde{R}$ as a function of $E_J/E_C$ in the main plot and as a function of the magnetic flux $\mathrm{\Phi }$ in the inset plot.

Figure 5

The switching voltage as a function of $E_J$ for arrays A255 (magenta), B255 (red), and C255 (blue).

Figure 6

Comparison of switching voltage extracted from single sweeps (blue dots) and full switching voltage histograms (red symbols). The data displayed in red show the width of the histograms (see text for an explanation).